Is there a notation for element-wise (or pointwise) operations? For example, take the element-wise product of two vectors x and y (in Matlab, x .* y, in numpy x*y), producing a new vector of …

Jul 8, 2019 · When talking vectors/matrices/tensors, pointwise is best avoided because it is decently ambiguous, since vectors can be interpreted as points. So a pointwise multiplication …

The pointwise convergence depends on each x x, that is you need to count and fix every x x before passing to the limit. On the other hand, uniform convergence is independent of x x.

The second one is uniform continuity, ive just forgot to change the name (because i copied and modified from the pointwise version). Thanks anyway.

Sep 25, 2015 · Similarly, you could say that vector addition is 'pointwise addition' because you're adding the entries in parallel according to their indices. In the article, rather, it is just using it to …

Feb 9, 2025 · For pointwise convergence everywhere, x x is picked first, then an N N is found which works for that x x. Different values of x x can have different N N. With convergence in …

Oct 3, 2020 · Sequence of continuous functions on $ [0,1]$ pointwise converging to an unbounded function Ask Question Asked 5 years, 3 months ago Modified 2 years, 3 months ago

Apr 21, 2021 · Commented Apr 28, 2012 at 14:10 1 Choosing suitable intervals with length going to zero you can exhibit a sequence of L^p, but pointwise the sequence doesn't converges at …

Jul 25, 2021 · Intuitively I feel like that weak convergence only controls the behavior of integral (by Riesz Representation Theorem), which cannot affect pointwise structure. But I don't know how …

Everywhere pointwise convergence is necessary to guarantee that fn → f f n → f pointwise if every subsequence has a further subsequence which converges to f f pointwise. With that …